Question
Real Tutor Solution
Tutor-Verified Answer
Answer
\( x = 1 \)
Solution
To solve the equation:
\[
\frac{11x}{3x + 8} = 1
\]
**Step 1: Eliminate the Denominator**
Multiply both sides of the equation by the denominator \( 3x + 8 \) to eliminate the fraction:
\[
\frac{11x}{3x + 8} \times (3x + 8) = 1 \times (3x + 8)
\]
Simplifying both sides:
\[
11x = 3x + 8
\]
**Step 2: Collect Like Terms**
Subtract \( 3x \) from both sides to gather the \( x \)-terms on one side:
\[
11x - 3x = 8
\]
\[
8x = 8
\]
**Step 3: Solve for \( x \)**
Divide both sides by 8 to isolate \( x \):
\[
x = \frac{8}{8} = 1
\]
**Step 4: Verify the Solution**
It's good practice to check if the solution satisfies the original equation and doesn't make the denominator zero.
Substitute \( x = 1 \) back into the denominator:
\[
3x + 8 = 3(1) + 8 = 11 \neq 0
\]
Since the denominator is not zero, \( x = 1 \) is a valid solution.
**Answer:**
\[
x = 1
\]
Reviewed and approved by the UpStudy tutoring team
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Simplify this solution Mind Expander
To solve for \( x \) in the equation \( \frac{11x}{3x+8} = 1 \), start by eliminating the fraction. You can do this by multiplying both sides by \( (3x + 8) \), giving: \[ 11x = 3x + 8. \] Next, isolate \( x \) by moving \( 3x \) to the left side: \[ 11x - 3x = 8, \] which simplifies to: \[ 8x = 8. \] Now, divide both sides by 8: \[ x = 1. \] Thus, the solution to the equation is \( x = 1 \).
